ABSTRACT
In this paper we seek to apply the methods of monotone dynamical systems theory to a model of microbial competition for a nutrient in a tubular reactor that was formulated by Kung and Baltzis(1992). The model takes the form of a reaction diffusion system describing the time evolution of the concentrations of nutrient and two competing populations of microorganisms in the reactor. Kung and Baltzis studied the system using numerical simulations and their work strongly suggests that both populations can coexist in a stable steady state for a restricted set of parameter values. Here we use analytical methods to prove this assertion. The analysis follows that of Smith(1995) and is similar to an analysis of a related model of So and Waltman(1989) which was studied by Hsu and Waltman(1993) and Hsu, Smith and Waltman(1995).
